# Maximum particle displacement in a sonic boom wave

• markmai86
In summary, to find the maximum particle displacement for a typical sonic boom, the equation ParticleDisplacement = SoundPressure / (SpeedOfSound*AirDensity*2*PI*SoundFrequency) can be used, where the speed of the wave (u) is represented by the equation u = p * C0 * rho0 or u = c0 * S, and the formula velocity = wavelength * frequency can be used to bring together the velocity of the wave, its wavelength, and its frequency. The units should also be checked when using these equations.
markmai86

## Homework Statement

A typical sonic boom is a solitary N wave with a peak to peak pressure amplitude of 2 lbf/ft^2 and a wavelength of 50 ft. Find the maximum particle displacement.

None

## The Attempt at a Solution

I've found some equations on the internet. For instance, I have the speed of the wave (u) (that I should then differentiate to get the particle displacement I think...):
u = p * C0 * rho0
or
u = c0 * S
I can't manage anyhting with these equations and I can't find anything representing the sound wave of the problem on a graph. I can't visualize the problem at all.
Could anyone give me some tips or explanations on this problem?

Thank you

Carid said:
I found this expression here

http://en.wikipedia.org/wiki/Particle_amplitude

ParticleDisplacement = SoundPressure / (SpeedOfSound*AirDensity*2*PI*SoundFrequency)

Thank you for the formula, but this formula includes the Sound frequency and the sound pressure which are not in the problem statement. Is it something I should know or I could find on the internet?

Thank you

Last edited:
Do you know any formula which brings together the velocity of a wave, its wavelength and its frequency?

As for pressure, doesn't the question include this information?

Sorry about the sound pressure, I wrote that maybe a little too fast.

As for the formula you are talking about is it:

velcity = wavelength * frequency

?

Yes, that's the one

Alright I think everything is working out, I'll just have to check the units as I'm not very familiar with it.

Thank you very much

## 1. What is maximum particle displacement in a sonic boom wave?

Maximum particle displacement in a sonic boom wave refers to the maximum distance that particles in the air are displaced from their original position as a result of a sudden change in air pressure caused by a supersonic object.

## 2. How is maximum particle displacement in a sonic boom wave measured?

Maximum particle displacement in a sonic boom wave is typically measured in units of pressure, such as pounds per square inch (psi), using specialized instruments called microphones or pressure sensors.

## 3. Can maximum particle displacement in a sonic boom wave cause damage?

In most cases, maximum particle displacement in a sonic boom wave is not strong enough to cause any significant damage to structures or objects. However, in rare cases, it can cause minor damage to windows or fragile objects.

## 4. What factors can affect the maximum particle displacement in a sonic boom wave?

The maximum particle displacement in a sonic boom wave can be influenced by a variety of factors, including the speed and altitude of the supersonic object, the atmospheric conditions, and the distance from the source of the sonic boom.

## 5. How can maximum particle displacement in a sonic boom wave be reduced?

There are several methods that can be used to reduce the maximum particle displacement in a sonic boom wave, including designing aircraft with more aerodynamic shapes, using noise-reducing materials, and flying at higher altitudes.

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